Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Combinatorics and Probability Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. The number of ways to distribute 5 identical balls into 3 distinct boxes (allowing empty boxes) is:

    Answer: 21

    By stars and bars, C(5+3−1, 3−1) = C(7, 2) = 21.

  2. How many distinct diagonals does a convex octagon have?

    Answer: 20

    Diagonals = C(8, 2) − 8 = 28 − 8 = 20.

  3. A function f: {1, 2, 3} → {1, 2, 3} is chosen at random. What is the probability it is a bijection?

    Answer: 2/9

    There are 3³ = 27 total functions and 3! = 6 bijections, so P = 6/27 = 2/9.

  4. If 5 fair dice are rolled, what is the probability all show different faces?

    Answer: 5/54

    P = (6 × 5 × 4 × 3 × 2)/6⁵ = 720/7776 = 5/54.

  5. In a group of 30 people, the probability that at least two share a birthday is approximately:

    Answer: Greater than 70%

    The birthday problem gives approximately 70.6% for 30 people.

  6. What is 0! (zero factorial)?

    Answer: 1

    By convention (and the gamma function), 0! = 1.